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Correction of ADCP compass errors resulting from iron in the instrument’s vicinity
Wilken-Jon von Appen
∗
Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany
accepted at Journal of Atmospheric and Oceanic Technology
November 6, 2014
∗
Corresponding author address: Wilken-Jon von Appen, Alfred Wegener Institute Helmholtz Centre for
Polar and Marine Research, Am Handelshafen 12, 27570 Bremerhaven, Germany. E-mail:
[email protected]
1
ABSTRACT 1
Iron in the vicinity of compasses results in compass deviations. ADCPs mounted on steel
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buoyancy devices and deployed on seven moorings on the East Greenland outer shelf and
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upper slope from 2007 to 2008 suffered from severe compass deviations as large as 90◦
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rendering the ADCP data useless without a compass correction. The effects on the measured
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velocities, which may also be present in other oceanic velocity measurements, are explained.
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On each of the moorings, velocity measurements from a different instrument are overlapping
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in space and time with the compromised measurements. The iron was not in the vicinity
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of this second instrument and the instrument is therefore assumed not to be affected by
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compass deviations. A method is described to determine the compass deviation from the
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compromised and uncompromised velocity measurements and the compromised compass
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headings. The method depends on the assumptions that at least one instrument per mooring
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is not compromised and that the change in flow direction over the vertical distance from the
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compromised to the uncompromised velocity measurement is zero on average. With this
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method, the compromised headings as well as the compromised velocity records can be
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R corrected. The method is described in detail and a Matlab function implementing the
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method is supplied. The success of the method is demonstrated for a mooring with a minor
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compass deviation and for one with a large amplitude deviation.
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1. Introduction
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Steel can exhibit two different magnetic behaviors related to the iron it contains: Mag-
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netically hard iron keeps the magnetic field that had been imparted on it during its formation
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(e.g. when it cooled from the liquid phase). Soft iron, on the other hand, allows its magnetic
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dipoles to align with the ambient magnetic field (e.g. the Earth’s magnetic field). Compasses
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point in the direction of the ambient magnetic field which is the sum of the Earth’s magnetic
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field and the magnetic field of any iron (both hard and soft) in addition to other magnetic
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materials and electromagnets present. If a significant amount of iron is in the vicinity of a
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compass, the direction in which the compass will point may be substantially different from
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magnetic north (as indicated by the field lines of Earth’s magnetic field). The error due to
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this effect can be as large as the full range of achieved instrument headings.
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A common setup in oceanographic moorings is to have an ADCP mounted on a buoyancy
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device. The ADCP may be looking up or down from its location in the mooring. Syntactic
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foam spheres contain a small amount of steel (and hence iron) and are comparably expensive.
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Steel spheres, on the other hand, are more economical (approximately half the price of
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syntactic foam spheres), but, by design, contain large amounts of iron. The setup as shown
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in Figure 1 where the ADCP is attached to the sphere, and is hence separated by less than
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0.5 m, was employed in a mooring deployment in 2007. Since an integral component of any
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velocity measurement is the determination of the instrument orientation using its compass,
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the compass deviation due to the iron in the vicinity has a direct effect on the velocity
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measurements. There are likely many mooring setups in which this introduces small errors
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in the velocity measurements, but there are also several mooring setups where the resulting
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errors are large.
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Pre- and/or post-cruise calibration on land of the ADCP compass is advisable, but may
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not be sufficient to deal with this problem. The effects of hard steel can be dealt with
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using such a calibration, but the behavior of the soft steel may be significantly different
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if the absolute magnitude of the Earth’s magnetic field and/or the ratio of its horizontal 2
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to its vertical component is significantly different between the deployment location and the
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calibration location on land. This would specifically be applicable for deployments at high
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latitude (in the Arctic or Antarctic) and calibration at lower latitudes.
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In the deployment of an array of seven moorings across the East Greenland outer shelf and
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upper continental slope, a particularly bad case of this compass deviation was encountered.
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The order of magnitude of this effect was that for the full 360◦ that each of the compasses
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on the moorings should have recorded for at least a very short time during the deployment
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year, some ADCP compasses only ever measured directions within a 100◦ range. This means
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that the other 260◦ of possible directions received zero counts1 . However, the moorings also
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contained a second instrument (an ADCP on some of the moorings and an ACM—Acoustic
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Current Meter—on the other moorings) measuring velocities from an instrument location
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which was at least several meters removed from the steel spheres. Some of the velocity
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measurements from the two instruments were spatially and temporally in close proximity.
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In the following, we assume that the compass of the lower instrument was not affected by the
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steel sphere. This assumption cannot explicitly be verified. However, there are no indications
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in the records to suggest that they were affected (the full 360◦ of compass headings were
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recorded). Furthermore, the resulting scientific results (e.g. Harden et al. 2014; von Appen
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et al. 2014a,b) are self-consistent and consistent with previous studies of the dynamics in the
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region based on shipboard surveys, sea surface temperature observations, numerical models,
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and theory. This provides confidence that the assumption that the lower instruments are
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not affected is correct.
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This paper documents a method that uses theory about compass deviations together
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with the overlapping velocity measurements to correct the ADCP velocities. While it is
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not clear how often this specific setup has occurred elsewhere, we believe that the current
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approach may be helpful to improve the data quality of other ADCP records compromised in We note that similar effects (compass ranges of only ≈100◦ ) can also result from incorrect lookup tables in the instruments’ firmware. If the resulting biases are only heading dependent, the methods described in this paper could also be applied in those situations. 1
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a similar manner as long as some independent information about the flow field measured by
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the compromised instrument exists. One such setup might be a lowered ADCP mounted on
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a CTD rosette under the influence of the steel in the rosette frame and the attached weights.
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In this case, measurements from a vessel mounted ADCP may be used as an independent
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uncompromised record of the overlapping ocean current velocities to correct the compass
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deviation of the lowered ADCP’s compass. This correction would precede the conventional
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processing step of applying vessel mounted ADCP measurements as a constraint to the
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inversion of lowered ADCP data.
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2. Description of the mooring setup
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From September 4th, 2007 to October 4th, 2008, seven moorings were deployed across
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the outer shelf and upper continental slope of East Greenland between 65◦ 30.0’N 33◦ 8.8’W
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and 65◦ 7.3’N 32◦ 41.1’W. The exact mooring positions and instrument configurations are
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provided in Table 1 and a cross-sectional view of the mooring array is shown in Figure 2.
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EG4 (the fourth mooring) contained the largest number of individual instruments and its
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design is shown in Figure 3. The other moorings were identical except that they were missing
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some of the instruments as detailed in Table 1 and that the 5/16” Jac Nil Wirerope was
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a different length to achieve the position of the steel sphere at ≈100 m depth. All of the
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moorings were designed to measure velocity between the bottom and the surface. At each
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of the moorings, a top buoyancy sphere made of steel was moored in ≈100 m depth and an
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upward looking 300 kHz Teledyne RD Instruments (RDI) Workhorse ADCP was attached
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to the sphere. Figure 1 shows a photo of how the ADCP was attached to the sphere.
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Upward looking 300 kHz RDI Workhorse ADCPs were moored on the bottom of EG1 and
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EG2. EG3 and EG4 had upward looking 75 kHz RDI Long Ranger ADCPs on the bottom
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and EG4 also had a downward looking 75 kHz RDI Long Ranger ADCP attached to the
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mooring cable >1 m below the steel sphere. McLane Moored Profilers (MMPs) containing
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a Falmouth Scientific, Inc. (FSI) Acoustic Current Meter (ACM) each operated between
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the bottom and the steel sphere on EG5–7. The profilers on EG5–7 therefore measured
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velocity as well as conductivity/temperature/pressure. Instead of the MMPs, EG1–4 had
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Coastal Moored Profilers (a Woods Hole Oceanographic Institution in-house development)
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which only measured conductivity/temperature/pressure.
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This means that at all moorings velocity was measured closely above the steel spheres
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by the first bin of the attached upward looking ADCPs and closely below. On EG1–3, the
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measurement below was achieved by the distant bins of the upward looking ADCPs and on
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EG4 by the first bin of the downward looking ADCP. On EG5–7, the measurement below
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was achieved by the MMPs when they were near their top bumper stop. While we realize
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that there is shear and short term temporal variability, we considered measurements above
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and below the sphere separated by less than 20 minutes in time and 20 m in the vertical to
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be overlapping. These overlapping velocity measurements should, on average, measure the
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same flow speed and direction. This is one assumption used in this paper and the second is
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that the lower instruments were not affected by compass deviations.
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The currents on the upper continental slope turned out to be stronger than anticipated
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during the design of the moorings. This resulted in frequent large amplitude mooring motion.
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Some of the top buoyancy spheres were blown down from their target water depth of 100 m
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to more than 400 m depth. This complicated the interpretation of the data and also caused
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the moored profilers to miss profiles as they were stuck during strong blowdown events, but
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it also allowed for the identification of large velocity events associated with the passage of
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Denmark Strait Overflow Water cyclones (von Appen et al. 2014a). However, because the
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steel sphere is at the top of the mooring, the tilt (combined roll and pitch) of the upward
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looking top ADCPs never exceeded 10◦ and was typically around 5◦ . Since these tilt values
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are not atypically large and because the compass deviation also occurred on the shallowest
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mooring EG1, which—being on the shelf—was not subject to significant blowdowns, we
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conclude that the compass deviation is not related to the blowdowns.
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3. Theory of magnetic compass deviation
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The combined effects of different configurations of iron in the vicinity of a compass lead
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to a compass deviation. A compass deviation is the difference between the correct heading
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to magnetic north and the uncorrected heading recorded by the compass. This compass
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deviation is a function of the direction with respect to magnetic north. The geometry of the
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iron in the vicinity of the compass can be decomposed into a symmetric and an asymmetric
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part (National Geospatial-Intelligence Agency 2004)2 . Geometrical considerations show that
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any geometry can in general be described as the sum of these two parts. The two parts have
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different influences on the compass, but their sum has a special functional form with only
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five independent parameters:
β − γ(β) = A + B sin(β) + C cos(β) + D sin(2β) + E cos(2β).
(1)
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Here β is the correct heading to magnetic north and γ is the uncorrected heading of the
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compass needle as defined in Figure 4. Following National Geospatial-Intelligence Agency
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(2004), the constant A is a bias resulting from physical misalignments of the compass. The
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coefficients B and C associated with the semicircular sin(β) and cos(β) describe the effects
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of the permanent magnetic field of hard iron. Finally, induced magnetism from soft iron
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contributes to all five coefficients A, B, C, D, and E . As such it is not possible to conclude
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from a particular compass deviation curve whether hard or soft iron effects dominate. The
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remainder of this paper derives a method to determine these five constants and to then use
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them to correct the compass headings.
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Mechanisms developed to correct the compass deviation due to such steel geometries are
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typically applied to ships’ compasses (e.g. National Geospatial-Intelligence Agency 2004)
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as they treat ships as sums of symmetric and asymmetric arrangements of hard and soft
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steel in the vicinity of the compasses. A steel sphere in the vicinity of an ADCP is nothing 2
This handbook (National Geospatial-Intelligence Agency 2004) provides useful background and details about compass corrections as they are standard on ships.
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else. Therefore we consider the theory developed for ships to also be applicable for ADCPs
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in the vicinity of steel spheres. Note that this assumes that the ship or steel sphere does
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not roll or pitch. Roll and pitch lead to a tilting of the steel arrangement relative to the
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Earth’s magnetic field. The coefficients A through E do not account for the effect of tilt.
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We justify this omission by the fact that, since the ADCP was at the top of the moorings,
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the instrument tilt was recorded to be small (between 3◦ and 10◦ ). The compass heading
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error due to these values of the tilt is an order of magnitude smaller than the effects of the
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iron.
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Just as in a ship, there is a forward direction to an ADCP. The ADCP measures currents
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in the instrument’s reference frame (instrument coordinates) for which, by convention, beam
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3 is forward. Using beam 3 as the instrument forward direction, β (beta) is the ADCP’s
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corrected heading (Figure 4) and γ (gamma) the uncorrected heading (relative to magnetic
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north). Any differences between β and γ are due to compass errors. Figures 5, 6a, and 7a
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shows this pointing error (compass deviation) as a function of the beam 3 direction. Figure 5
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shows a range of synthetically constructed compass deviations with differing amplitudes.
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Figure 6a shows real data from mooring EG2 for a case with a small compass deviation and
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Figure 7a is data from EG4 with a large amplitude compass deviation case. For the following discussion we introduce a few directions and angles, all of which are
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defined with respect to the ADCP’s forward direction and sketched in Figure 4:
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• a: Forward direction of ADCP, beam 3 pointing direction.
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• b: Current direction, direction in which the water is moving.
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• c: Magnetic north, the heading of a correctly compensated compass.
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• d: Direction in which uncorrected compass points.
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• e: Geographic north, lines of constant longitude.3 3
The equivalent terms used in the handbook of the National Geospatial-Intelligence Agency (2004) are: “ship’s heading” for a, “magnetic meridian” for c, and “true meridian” for e.
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• α: Angle between b and a, current direction in instrument coordinates.
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• β: Angle between a and c, correct heading to magnetic north in instrument coordinates.
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• γ: Angle between a and d, uncorrected ADCP compass heading. This is what the
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ADCP incorrectly records as its magnetic heading. Note that this does not yet account
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for the declination δ which is only applied during processing on shore after the recovery.
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• δ: Angle between c and e, declination, also known as variation. This is the difference
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between the directions to magnetic north and geographic north. For oceanographic
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purposes, it is a known geophysical external parameter that for any location and time
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on Earth can be retrieved from a numerical model such as http://ngdc.noaa.gov/
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geomag/magfield.shtml.
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The quantities measured during the deployment with two overlapping instruments as de-
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scribed in the previous section can be expressed in terms of the above defined directions and
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angles:
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• γ: Uncorrected heading of upper ADCP.
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• Dbot : Current direction of lower ADCP/ACM after onshore processing including cor-
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rection for magnetic declination δ. This current direction measurement is assumed not
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to be affected by a compass deviation.
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• Dtop = α + γ + δ: Current direction of upper ADCP after onshore processing that was affected by a compass deviation.
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corr The correct current direction of the upper ADCP would be Dtop = α + β + δ. But if, as
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assumed, the records from the two instruments are overlapping, then the correct current
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corr directions from the two instruments should be identical, i.e. Dtop = Dbot .
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The following quantities are needed to construct the compass deviation curve as defined in Equation (1): 8
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Forward direction of upper ADCP in correct magnetic earth coordinates:
corr β = (α + β + δ) − (α + γ + δ) + γ = Dtop − Dtop + γ = Dbot − Dtop + γ
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(2)
Compass deviation (magnetic deviation of compass due to the presence of iron in its vicinity):
corr β − γ = (α + β + δ) − (α + γ + δ) = Dtop − Dtop = Dbot − Dtop
(3)
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To illustrate the results of compass deviations, Figure 5 shows synthetic compass de-
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viation curves. To keep the discussion simple, we considered only a simplified version of
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Equation (1) where A, C, D, and E are set to zero and B varies over a range of typical
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values.
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The mapping from the correct magnetic compass direction to the compass deviation is
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called the uncompensated compass deviation curve β → β − γ and shown in Figure 5a
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for the synthetic cases. There are two special regions on the compass deviation curve. The
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compass behavior is “sluggish” where for a given change in correct instrument heading β, the
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uncorrected heading γ changes by a smaller amount, that is
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Intelligence Agency 2004). Conversely, the behavior is “unsteady” in the region where γ
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changes by a larger amount than β:
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vicinity of β = 0◦ (Figure 5b) while the unsteady region is near β = ±180◦ .
∂γ ∂β
∂γ ∂β
< 1 (National Geospatial-
> 1. In the example, the sluggish region is in the
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When the uncompensated compass deviation curve β → β − γ has been constructed,
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the relationship between correct and uncorrected heading can be plotted as β → γ and
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then inverted as γ → β. If the compass deviations are of large amplitude, the response of
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the compass changes sign. That is for an increase in the uncorrected heading, the correct
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heading actually decreases:
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than 180◦ /π ≈ 57.3◦ . In those cases, the inversion is no longer unique and β(γ) becomes
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multivalued. In this case, the inversion can only be carried out in the region of maximum
∂γ ∂β
< 0. In the synthetic case this happens for values of B larger
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sluggishness and the lookup table β(γ) will not be defined for all uncorrected headings γ.
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In order to see the effect of the compass deviations shown in Figure 5 on the measured
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velocities, consider the velocity that is recorded by the instrument for an ocean velocity that
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is aligned with the forward direction of the instrument, i.e. α = 0. For simplicity, we also
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assume δ = 0 here. For a correct heading of 0◦ , all of the synthetic compass deviations would
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not affect the recorded ocean current directions and they would always correctly be recorded
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as 0◦ . However, for the same α = 0 and a correct heading of β = 90◦ , the recorded velocities
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would be: α + γ + δ = α + β − (β − γ) + δ = 90◦ − B. The synthetic compass deviations
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with amplitudes of B = 0◦ , 20◦ , 45◦ , 57.3◦ , 90◦ , and 135◦ would result in recorded current
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directions of 90◦ , 70◦ , 45◦ , 33.7◦ , 0◦ , and -45◦ , which clearly would be disastrously different
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from the correct current direction of 90◦ for any compass deviation much bigger than 20◦ in
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amplitude.
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However, if β(γ) (the correct heading β corresponding to the uncorrected heading γ)
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can be determined, the ADCP compass can be corrected in order to obtain the corrected
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upper current direction:
corr Dtop = α + β(γ) + δ = (α + γ + δ) + β(γ) − γ = Dtop + β(γ) − γ
(4)
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A lookup table for β(γ) must be constructed. For the γ for which β(γ) is defined, the upper
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current direction can be corrected, while it is not possible for the γ for which β(γ) is not
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defined and those current directions must be marked as N aN s. The correction according
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to Equation (4) can be applied to any extended data set from the upper ADCP and is not
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limited to the overlapping times and depths.
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4. Application of method to mooring data The correction method involves the following steps which have been implemented in a R Matlab function that is supplied in the supporting online material.
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• Construct a scatter plot based on the overlapping measurements of β → β − γ.
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• Use the Matlab curve fitting toolbox to fit a smooth line obeying Equation (1) to the
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scatter. This might for example also be done with Python’s scipy.optimize.curve fit
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package.
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• Use the fitted curve of β → β − γ to plot β → γ.
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• If the compass deviation is of small amplitude such that γ → β is not multivalued,
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invert the curve and plot it.
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• If the compass behaves very sluggish (only a smaller range of headings than the ex-
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pected range was recorded), then the same compass deviation γ can refer to different
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correct headings β and β → γ becomes multivalued. The greatest information is then
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contained in the region of maximum sluggishness. This region has to be selected for
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the inversion. ∂γ ). ∂β
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• Invert the curve in the sluggish region (around the minimum of
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• The lookup table of β(γ) has been achieved and can be used to correct the upper
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corr current direction: Dtop = Dtop + β(γ) − γ.
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• To assess the success of the compass correction, plot histograms of the upper uncor-
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rected as well as the upper corrected headings along with histograms of the upper
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uncorrected, the upper corrected, and the lower current directions. A scatter of the
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upper uncorrected and corrected versus the lower current direction allows for an as-
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sessment by how much the correlation has improved.
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The method has been applied successfully to all seven moorings on the East Greenland
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shelf and slope. For illustrative purposes, we present a case with only a minor compass devi-
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ation (mooring EG2) and a case with a large amplitude compass deviation (mooring EG4).
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The uncompensated compass deviation curve β → β − γ for EG2 (Figure 6a) is constructed
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as a scatter plot of all the overlapping data points. These are defined as the measurements
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from the upper and lower instrument that were separated by less than 20 minutes in time
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and less than 20 m in the vertical. In the case of EG2, the compass deviation is small and
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therefore most of the data points are within 45◦ of 0◦ . The scatter is due to the slight offset
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in measurement time and location as well as to noise and other non-systematic measurement
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errors. For mooring EG4, the compass deviation is large and the data scatter (Figure 7a)
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therefore does not cluster around 0◦ . A nonlinear least squares fit to Equation (1) is ap-
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plied to the data scatter resulting in the red curve. As the curve is invertible for all correct
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headings β, in the small compass deviation case (Figure 6a), the red curve is overlain by
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the green curve indicating the invertible region. In order to find the region where the fitted
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compass deviation curve can be inverted, the correct heading β is subtracted from the fit
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and plotted versus the correct heading β (Figures 6b and 7b). The inversion from β → γ to
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γ → β in the small amplitude case is straightforward as it is everywhere defined (Figure 6c).
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For EG4, however, γ → β is multivalued. This is due to the fact that the amplitude of
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the compass deviation was as large as 100◦ . This means that there is even a reversal of the
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compass response, i.e. when the correct heading is increasing, the uncorrected heading is
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actually decreasing:
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In this region, the compass only traced a small range of directions (≈55◦ ), but because of the
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sluggishness, this actually corresponds to a much wider range (≈185◦ ) of correct instrument
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headings. The lookup table (Figure 7c) to convert an uncorrected heading γ to the correct
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heading β is then simply the inversion in the sluggish region. The scatter in Figure 7a would
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also suggest to use a linear fit. However, this would result in ambiguities as e.g. β = −180◦
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would be mapped to β − γ ≈ −310◦ and β = 180◦ would be mapped to β − γ ≈ 150◦ which
∂γ ∂β
< 0 (green curve in Figure 7b). The compass is extremely sluggish.
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even taking into account the 360◦ periodicity are completely different values. How would one
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then choose the correct one? Rather than using such a visually suggested linear fit, the fit to
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Equation (1) provides a physically based recipe for applying a compass correction. The semi-
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circular contribution to the compass deviation curve (parameters B and C in Equation (1))
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clearly is large, but as mentioned before, it is not possible from this to assess whether the
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compass deviation due to hard or soft iron was more severe. The fact that there are only a
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few instrument headings outside of this ≈185◦ range of correct headings is due to the fact
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that the mooring was embedded in a mostly unidirectional flow (actually a narrow band
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variability around that major direction) and the ADCP representing the biggest asymmetric
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drag on the otherwise symmetric sphere was almost always located in the wake of the sphere
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consistent with the orientation of any asymmetric blunt object in a flow.
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The success of the method can be judged by comparing the current directions deter-
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mined by the upper ADCP before and after the compass correction to the current directions
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determined by the lower instrument. The compass correction in the case of EG2 is minor
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meaning that the histograms of the headings (Figure 8a) and current directions (Figure 8b)
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of the upper instrument do not change much and agree well with the lower current direc-
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tion. This is also obvious in the scatter plot (Figure 8c) where one would conclude that
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both the uncorrected and the corrected upper current directions reasonably agree with the
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lower current directions. However, the effect is relevant for EG4. The histogram for the
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headings (Figure 9a) shows the increase of the range of headings from the uncorrected to the
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corrected situation and also the extremely sluggish behavior of the compass. The long tail of
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the uncorrected headings γ is to the left of the peak, while it is to the right of the peak of the
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corrected headings β. This is due to the fact that the correct heading actually decreases for
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an increase in the uncorrected heading (Figure 7b). The histogram of the upper uncorrected
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current directions (Figure 9b) has little resemblance of the lower current directions, while the
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agreement is much improved with the correction. This is also true for the direct scatter plot
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(Figure 9c) where a majority of the scatter now falls in the vicinity of the straight line that
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would be applicable if there was no compass deviation or conversely if the correction was
313
perfect. Obviously, the method is not perfect, but leads to a much improved determination
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of the upper current direction.
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However, the developed method fails to determine the correct instrument heading for
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some recorded uncorrected instrument headings located outside of the invertible region of
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the fitted curve (Figure 7a). For those headings, a correction of the velocity is not possible.
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This leads to a biased (as a function of instrument heading and therefore most likely current
319
direction) exclusion of data. While this is unfortunate, the method uses a physically justi-
320
fied procedure to determine the correct current direction for the majority of the top ADCP
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data. For 7873 hourly records at mooring EG4, the compass directions could successfully
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be corrected and the correction failed in 13% of the measurements. For the other moorings,
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the failure rate ranged from 0% to 30%. Since there were many times when only the upper
324
ADCPs recorded velocity (e.g. because the MMPs only sampled twice a day and were some-
325
times stuck at depth while the ADCPs sampled hourly), this method made large amounts
326
of data usable in addition to the overlapping recordings.
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5. Conclusions
328
A method has been described to correct velocity measurements affected by compass
329
deviations caused by iron in the instruments’ proximity. It is likely that errors to oceanic
330
velocity measurements due to compass deviations are rather frequent, although not of as large
331
an amplitude as presented here. This should therefore be considered in the error discussion
332
of oceanic velocity measurements. Where overlapping uncompromised measurements are
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R available, the method (including the ready to use Matlab function) presented here may be
334
used to improve data quality or to make data usable in the first place.
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While this paper has focused on correcting the compass deviation after data acquisition,
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we would also like to raise awareness of the problem in the first place. This will hopefully help
14
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to limit these problems during the mooring design phase. Physically separating compasses
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from large bodies of iron such as steel spheres is the most effective way to avoid compass
339
deviations. Even a separation by a few meters is highly beneficial. If a physical separation is
340
not possible, it is advised to test for the compass deviation prior to deployment and possibly
341
choose configurations with smaller amplitude compass deviations.
342
Acknowledgments.
343
Discussions with Robert Pickart, Benjamin Harden, Frank Bahr, and Daniel Torres of the
344
Woods Hole Oceanographic Institution were instrumental in the development of this work.
345
Thomas Haine and three anonymous reviewers provided very valuable comments on the
346
manuscript. Support for this study was provided by the U.S. National Science Foundation
347
(OCE-0726640) and the German Federal Ministry of Education and Research (0F0651 D).
348
APPENDIX
349
R The supporting online material contains a Matlab function called compass_correction.m
350
that implements the method described in the paper. It is accompanied by two functions
351
plot_analysis.m and plot_results.m plotting the compass correction curve and an as-
352
sessment of the success of the correction, respectively. The non-linear least squares fit to
353
Equation (1) is achieved using the Matlab curve fitting toolbox. An open source alterna-
354
tive is to use curve fit from Python’s scipy.optimize package for this part of the calcula-
355
tion or the whole calculation. However, due to the fact that Matlab is commonly used
356
in the oceanographic community, we only provide a Matlab function here. The help of
357
compass_correction.m provides a usage example that can directly be executed from the
358
Matlab command prompt.
359
The average velocity and depth of the first two bins above the upper ADCP was taken
360
at the measurement times (hourly sample rate). The same was done for two bins of the 15
361
lower current meter. These depths varied over time due to vertical mooring motion. All
362
the measurements from the two instruments that were separated by less than 20 minutes in
363
time and 20 m in the vertical were considered to be overlapping. By not using a fixed depth
364
below the surface, this also explicitly incorporates times when the moorings were blown
365
down significantly. The overlapping records from all seven moorings were then interpolated
366
onto the same hourly grid returning N aN s where no data was within ±30 minutes of the
367
temporal grid. This data from the seven moorings is also supplied for testing of the Matlab
368
function. Its file name is example_vels.mat.
369
370
REFERENCES
371
Harden, B., R. Pickart, and I. A. Renfrew, 2014: Offshore Transport of Dense Water from
372
the East Greenland Shelf. Journal of Physical Oceanography, 44 (1), 229–245.
373
National Geospatial-Intelligence Agency, 2004: Handbook of Magnetic Compass Adjust-
374
ment. Tech. rep., National Geospatial-Intelligence Agency, Bethesda, MD, available at
375
http://msi.nga.mil/MSISiteContent/StaticFiles/HoMCA.pdf.
376
von Appen, W.-J., R. Pickart, K. Brink, and T. W. N. Haine, 2014a: Water Column Struc-
377
ture and Statistics of Denmark Strait Overflow Water Cyclones. Deep Sea Research I, 84,
378
110–126.
379
380
von Appen, W.-J., et al., 2014b: The East Greenland Spill Jet as an important component of the Atlantic Meridional Overturning Circulation. Deep Sea Research I, 92, 75–84.
16
17 524 m 894 m 1163 m 1378 m 1585 m
65◦ 23.2’ N 33◦ 1.0’ W
65◦ 20.0’ N 32◦ 57.3’ W
65◦ 16.2’ N 32◦ 52.7’ W
65◦ 12.3’ N 32◦ 47.0’ W
65◦ 7.3’ N 32◦ 41.1’ W
EG4
EG5
EG6
EG7
268 m
65◦ 26.6’ N 33◦ 4.5’ W
EG2
EG3
248 m
65◦ 30.0’ N 33◦ 8.8’ W
EG1
upward facing 100 m 300 kHz ADCP
upward facing 100 m 300 kHz ADCP
upward facing 100 m 300 kHz ADCP
upward facing 100 m 300 kHz ADCP
upward facing 100 m 300 kHz ADCP
upward facing 100 m 300 kHz ADCP
upward facing 100 m 300 kHz ADCP
20–92 m
20–92 m
20–92 m
20–92 m
20–92 m
20–92 m
20–92 m
ACM/MMP
ACM/MMP
ACM/MMP
downward facing 75 kHz ADCP
upward facing 75 kHz ADCP
upward facing 300 kHz ADCP
upward facing 300 kHz ADCP
–
–
–
104 m
524 m
268 m
248 m
102–1580 m
102–1373 m
102–1158 m
114–450 m
100–514 m
100–260 m
100–240 m
Table 1. The following mooring details are given: name of mooring, latitude, longitude, and water depth of the moorings along with the type, the approximate instrument depth, and the approximate measuring range of the upper ADCPs and the lower current meters. Name Latitude Water Upper ADCP Lower current meter Longitude depth Type Inst depth Meas range Type Inst depth Meas range
381
382
List of Figures 1
Photo of the mooring setup discussed in this paper prior to deployment at
383
sea. The upward facing ADCP and the Argos beacon are attached to the steel
384
sphere using a mount. Photo by Daniel Torres (Woods Hole Oceanographic
385
Institution).
386
2
20
Cross-sectional view of the East Greenland mooring array. The different in-
387
struments and their sampling schedules are explained in the legend. The
388
nominal depth range sampled by the CMPs and MMPs is shown in red. The
389
bottom depth along the mooring line, measured by the ship’s echo sounder,
390
is shown in black. The acronyms are as follows: CMP: Coastal Moored Pro-
391
filer, ACM: Acoustic Current Meter, MMP: McLane Moored Profiler, ADCP:
392
Acoustic Doppler Current Profiler, MC: Microcat. Figure from von Appen
393
et al. (2014a).
394
3
21
Diagram of mooring EG4. The distances in the vertical are not to scale, but
395
the wire lengths are indicated instead. The other moorings were similarly
396
designed, but, as detailed in the text, they were missing some instruments
397
compared to EG4. No swivels were used in the moorings. Figure designed
398
by John Kemp and drawn by Betsey Doherty (Woods Hole Oceanographic
399
Institution).
22 23
400
4
Definition sketch of the directions and angles mentioned in the text.
401
5
Synthetic compass deviation curves. A, C, D, and E of Equation (1) are set
402
to zero and B varies as shown in the legend of (a). (a) is the uncompensated
403
compass deviation curve, (b) is the inference from the fitted correction curve,
404
and (c) is the lookup table for β(γ). The curves are solid where they can be
405
inverted and dashed elsewhere.
24
18
406
6
Analysis plots for the compass correction of the ADCP on EG2 which ex-
407
hibited only a minor compass deviation. (a) is the uncompensated compass
408
deviation curve, (b) is the inference from the fitted correction curve, and (c)
409
is the lookup table for β(γ). The black line would apply if there was no com-
410
pass deviation. Note that since the deviation is minor, the fitted curve can
411
be inverted over the full range of uncorrected headings which is why the red
412
curve is identical to (and covered by) the green curve. Note that the plotting
413
limits of the periodic x-axis are chosen to best fit the data scatter into the
414
interior of the figure.
415
7
25
Same as Figure 6, but for EG4 which exhibited a large amplitude compass
416
deviation. Note that the fitted curve can be inverted only in a small range
417
(29◦ –84◦ ) of uncorrected headings.
418
8
26
Results of the compass correction of the ADCP on EG2. (a) shows histograms
419
of the headings before and after the correction, (b) shows histograms of the
420
lower and upper current directions, and (c) is a scatter plot of the upper
421
versus the lower current direction. Since the compass deviation is small, the
422
blue and red curves are close to each other. Note that the plotting limits of
423
the periodic x-axis are chosen to best fit the histograms into the interior of
424
the figure.
425
9
27
Same as Figure 8, but for EG4. Since the compass deviation is large, the blue
426
and red curves differ significantly, and the improvement in the correlation (c)
427
is indicative of the success of the compass correction.
19
28
Fig. 1. Photo of the mooring setup discussed in this paper prior to deployment at sea. The upward facing ADCP and the Argos beacon are attached to the steel sphere using a mount. Photo by Daniel Torres (Woods Hole Oceanographic Institution).
20
0
EG1
EG2
EG3
EG4
EG5
EG6
EG7
200 400
Depth [m]
600 800 1000 1200 1400 1600
CMP: TS 2x daily ACM/MMP: TS/vel 2x daily upward ADCP: vel hourly downward ADCP: vel hourly MC: TS every 30mins −10
−3
4 11 18 27 Cross−stream distance from shelfbreak [km]
37
/Volumes/wilkenHDD/Documents/WHOI/Greenland/Writing/2012_DSR_Paper/Figures/sidemap.m [28−Mar−2013 17:22:00] Fig. 2. Cross-sectional view of the East Greenland mooring array. The different instruments and their sampling schedules are explained in the legend. The nominal depth range sampled by the CMPs and MMPs is shown in red. The bottom depth along the mooring line, measured by the ship’s echo sounder, is shown in black. The acronyms are as follows: CMP: Coastal Moored Profiler, ACM: Acoustic Current Meter, MMP: McLane Moored Profiler, ADCP: Acoustic Doppler Current Profiler, MC: Microcat. Figure from von Appen et al. (2014a).
21
Fig. 3. Diagram of mooring EG4. The distances in the vertical are not to scale, but the wire lengths are indicated instead. The other moorings were similarly designed, but, as detailed in the text, they were missing some instruments compared to EG4. No swivels were used in the moorings. Figure designed by John Kemp and drawn by Betsey Doherty (Woods Hole 22 Oceanographic Institution).
e, geographic north c, correct heading/magnetic north
d, uncorrected heading
δ a, instrument forward direction
γ β α
b, current direction
Fig. 4. Definition sketch of the directions and angles mentioned in the text.
23
(b) inference from correction curve 180 γ: uncorrected heading
(a) uncompensated compass deviation curve 180
135
β−γ = Dbot−Dtop : deviation
90
B = 0°, no deviation B = 20° B = 45° B = 180°/π ≈ 57.3° B = 90° B = 135°
135 90 45 0 −45 −90 −135 −180 −180
45
−90 0 90 β: correct heading
180
0
(c) β(γ) lookup table
−45 180 β: correct heading
135 −90
−135
−180 −180
−135
−90 −45 β = D −D bot
0 45 90 +γ : correct heading
top
135
180
90 45 0 −45 −90 −135 −180 −180
−90 0 90 180 γ: uncorrected heading
Fig. 5. Synthetic compass deviation curves. A, C, D, and E of Equation (1) are set to zero and B varies as shown in the legend of (a). (a) is the uncompensated compass deviation curve, (b) is the inference from the fitted correction curve, and (c) is the lookup table for β(γ). The curves are solid where they can be inverted and dashed elsewhere.
24
(b) inference from fitted correction curve 180 γ: uncorrected heading
(a) uncompensated compass deviation curve 180
135
individual overlapping records fitted curve invertible region of fitted curve curve if no deviation was present
β−γ = Dbot−Dtop : deviation
90
135 90 45 0 −45 −90 −135 −180 −180
45
−90 0 90 β: correct heading
180
0
(c) β(γ) lookup table
−45 point of maximum unsteadiness point of maximum deviation −90 point of maximum sluggishness
β: correct heading
135
−135
−180 −180
−135
−90 −45 β = D −D bot
180
0 45 90 +γ : correct heading
top
135
180
90 45 0 −45 −90 −135 −180 −180
−90 0 90 180 γ: uncorrected heading
Fig. 6. Analysis plots for the compass correction of the ADCP on EG2 which exhibited only a minor compass deviation. (a) is the uncompensated compass deviation curve, (b) is the inference from the fitted correction curve, and (c) is the lookup table for β(γ). The black line would apply if there was no compass deviation. Note that since the deviation is minor, the fitted curve can be inverted over the full range of uncorrected headings which is why the red curve is identical to (and covered by) the green curve. Note that the plotting limits of the periodic x-axis are chosen to best fit the data scatter into the interior of the figure.
25
(b) inference from fitted correction curve 180 γ: uncorrected heading
(a) uncompensated compass deviation curve 180
135
individual overlapping records fitted curve invertible region of fitted curve curve if no deviation was present
β−γ = Dbot−Dtop : deviation
90
135 90 45 0 −45 −90 −135 −180 −180
45
−90 0 90 β: correct heading
180
0
(c) β(γ) lookup table
−45 180 β: correct heading
135 −90
−135
−180 −180
−135
−90 −45 β = D −D bot
0 45 90 +γ : correct heading
top
135
180
90 45 0 −45 −90 −135 −180 −180
−90 0 90 180 γ: uncorrected heading
Fig. 7. Same as Figure 6, but for EG4 which exhibited a large amplitude compass deviation. Note that the fitted curve can be inverted only in a small range (29◦ –84◦ ) of uncorrected headings.
26
(a) histogram of upper headings γ: uncorrected β: corrected 30
(c) correlation of current directions
20
90
10
0 −270
−180
−90 upper heading [°]
0
90
(b) histogram of current directions
number of occurrences
50 upper uncorrected upper corrected lower
40
upper current direction [°]
number of occurrences
40
30
0
−90
−180
−270 −270
20
uncorrected corrected curve if correction was perfect −180 −90 0 lower current direction [°]
90
10 0 −270
−180
−90 0 current direction [°]
90
Fig. 8. Results of the compass correction of the ADCP on EG2. (a) shows histograms of the headings before and after the correction, (b) shows histograms of the lower and upper current directions, and (c) is a scatter plot of the upper versus the lower current direction. Since the compass deviation is small, the blue and red curves are close to each other. Note that the plotting limits of the periodic x-axis are chosen to best fit the histograms into the interior of the figure.
27
(a) histogram of upper headings γ: uncorrected β: corrected
400 300
(c) correlation of current directions 90
200 100 0 −270
−180
−90 upper heading [°]
0
90
(b) histogram of current directions
number of occurrences
400 upper uncorrected upper corrected lower
300
upper current direction [°]
number of occurrences
500
0
−90
−180
−270 −270
200
uncorrected corrected curve if correction was perfect −180 −90 0 lower current direction [°]
90
100
0 −270
−180
−90 0 current direction [°]
90
Fig. 9. Same as Figure 8, but for EG4. Since the compass deviation is large, the blue and red curves differ significantly, and the improvement in the correlation (c) is indicative of the success of the compass correction.
28
